{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import binom\n",
    "import sdm as sdmlib\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "_phi_fn_cache = {}\n",
    "def phi_fn(n, H, r, d, steps=500):\n",
    "    key = (n, H, r, d, steps)\n",
    "    if key in _phi_fn_cache:\n",
    "        return _phi_fn_cache[key]\n",
    "    v = []\n",
    "    for _ in range(steps):\n",
    "        bs1 = sdmlib.Bitstring.init_random(n)\n",
    "        bs2 = bs1.copy()\n",
    "        bs2.flip_random_bits(d)\n",
    "        selected1 = address_space.scan_opencl2(bs1, r)\n",
    "        selected2 = address_space.scan_opencl2(bs2, r)\n",
    "        x = len(set(selected1) & set(selected2))\n",
    "        v.append(x)\n",
    "    mu = 1.0*sum(v)/len(v)\n",
    "    _phi_fn_cache[key] = mu\n",
    "    return mu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 1000\n",
    "sample = 1000000\n",
    "r = 451\n",
    "\n",
    "address_space = sdmlib.AddressSpace.init_random(n, sample)\n",
    "address_space.opencl_init()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [],
   "source": [
    "training_set = 200\n",
    "training_noise = 0.15\n",
    "training_value = training_set*(1-2*training_noise)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "174.66"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training_shared"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "activated_hls = phi_fn(n, sample, r, 0, steps=200)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "activated_hls = int(activated_hls+0.5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40 140.0 7 980.0 1066\n",
      "41 140.0 7 980.0 1066\n",
      "42 140.0 5 700.0 1068\n",
      "43 140.0 5 700.0 1068\n",
      "44 140.0 4 560.0 1069\n",
      "45 140.0 3 420.0 1070\n",
      "46 140.0 3 420.0 1070\n",
      "47 140.0 2 280.0 1071\n",
      "48 140.0 2 280.0 1071\n",
      "49 140.0 1 140.0 1072\n",
      "50 140.0 1 140.0 1072\n"
     ]
    }
   ],
   "source": [
    "x_values = range(40, 51)\n",
    "y_values = []\n",
    "for x in x_values:\n",
    "    dist = int(x*n/100.0)\n",
    "    shared = phi_fn(n, sample, r, dist, steps=250)\n",
    "    shared = int(shared+0.5)\n",
    "    print(x, training_value, shared, training_value*shared, activated_hls - shared)\n",
    "    y = binom.cdf(training_value*shared, activated_hls - shared, 0.5)\n",
    "    y_values.append(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
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J4KOfrKqT1mmSmM9bGYkEdqtfzG2vJl+Z5EcXcI7hemvrbfxyKMOM5UZruAEjlnmTsYlY7pTk95Pcaab6k0n+WXcPn1oAtmmJ4/65mTzplExeYX76BscCi7OK6/tksrfR5Zts/8pB+Zyq2s7kBDCxjHGfqrp/Jm8enTKtujXJ07r7sd39uu6+vLtv6u5ru/svuvtFmbyx8OaZbu6W5E3TBxCAJeruzyf5rqzdAPm0JF830sR83opIJLDrVNW3JvmnM1XP7O6rx47fgeGXxMnrHjWiqiq+eGBelnKTcSjTzVh/P8k/mKm+Jsk/7u6PriImOIItfNxX1T9M8sMzVc/r7kvmfR5gYyu8vk+S87fQ/sKsXTP5hCRfvqOIYI9a4rhPkldk7f3887r7VRs16O5rk3xzkg/NVN8/yTPmHx5wKN39kSRvHFRvNpFgPm9JJBLYjX5u5vff7e7fWtB5PjUo33OL7e+Stcue3JrJ5o3AFiz5JmOjOE7I5MLlK2aqr0/y+O7+i2XHA0eyZYz76Sap/y3JgY3a3pe1b0AAy7Os6/tPrlO3qaUVkqS7b0kyTDaetqOIYO9ayrivqgdmsjnrAVcNzj1qum/KzwyqnzafyIBteOugfP+R48znrcgxhz4Elu72M78/vqo2XM90xL3XafeQ7r5opvyhweenb/Ecw+Mvnb6OBWzNsiYXRlXVsUl+K2tvQm7KZDmj4cZPwM4tY9z/iyQPmv5+ayb7L9yywfHA4izr+v7iddpdu8XzDI+/wxbbAxPLGvdfM/j8D8c2Vh/xu5ns03RgX4X7VdXduvtvtxgrsHPDpQjvPHKc+bwVkUhgL/vgoHzWFtufeYj+gM1Z1k3GuqrqqEw2V/zGmeq/T/Id3f0H24gFOLRljPvZcxyV5N2Tt5i37NVV9eqZ8hu6+4nb6QhYuA+sUzfcTPFQhussb2VCEli++wzKW1qOtLuvrqqrktxxpvoeSSQSYPluHpSPHTnOfN6KWNqIvez9WfsldcZ048fN+spB+ZATlsDuMl0b8ZVJnjRT3Um+t7tfv5qoAIDt6O7PJrlsUH2XLXYzXMros9uPCFiCYbJwO28fDicvj173KGDR7joof3rkOPN5K+KNBHajJ2Q86zjmQVm77vEnM1nSYNZHZgvd/bmqekfWvgr5tZk8mbyh6eTjYwfVb9p0tMBu8dIkTx3UPaO7X7OCWADgSLWU6/upNyb5NzPlh2YT1/dJUlV3ycHrLG96jwVgjWWN+2Gy7+5bOWFVHZ/kiwbVY5OXwGI9clAeLnWUxHzeKkkksOt09/lbbVNVw6cOPt/db9lE0zdm7RfPU7O5G43HZO0rlJ9M8p5NtAMOtszJhS+oqp9J8sxB9Y939y9sMRZg65Yx7l+f5K+2HlpekuSBM+WfS3LeTHm4uRtwCEu+vv+/WZtIeGJV/WB337qJtt8yKF/c3ett4AwcwhLH/ccG5XOrqrp7s8smPjpr58ZuTPLxTbYF5qSqbp/kmwfVw82XZ5nPWwGJBPa61yZ5QZKTp+VHVdVXd/cfjjWYZi+fM6h+9SZvToCBJU8uHGj/I0l+clD9wu5+4VZjAbZuGeO+uy/PyFNMhzjPVYOqD2zl+wVYufMz2YTx/tPy6Un+ZZJXj7ZIUlUnJfnhQfUiNoIH5ms40Xh6km9L8puHaji9t3/2oPqPu/vGOcUGbN6Ls3aPs5uS/P4Gx5vPWwF7JLCndfenkgyfPn5VVW30OuSPJXnUTPmaTJ5WBA4DVfV9SV40qP6F7v7xVcQDAMxPd/99Dn5Y4KVV9Q/H2lTV0Ul+NWufUNyf5L/OP0Jgnrr7kiTvHlT/UlU9cL3jD5hOKL4wk6eTZ/3aHMODPaeqnl1VD93C8cdU1Uty8JLDr+ju0U3PzeethkQCTCYUr5wp3yfJu6rqm6YXF0mSqrpnVb0iyfMH7Z/f3X+3hDiBHaqq70jy8kH1q5M8YwXhAAAL0N3/O5M3Ew44NcnbquqZVXXK7LFV9RVJ3pLkSYNufmi6eTOw+z07yexSRndI8idV9VNVtWbz1qo6qqq+MpMnnZ816Ocvk/zPhUYKR75/kuRPq+qd07+7D6iqg1bEqapTq+rbk1yY5IcGH1+S5HmbOJf5vCWztBF7Xnf/XVX98yR/kOSEafW9k7whydVV9dFMXq86PcnRg+ZvyNr1moFdqqoem8kTRrNJ9A9m8trz18xcZ2zGVd393jmGBwDM17cneWdue8vglCQvS/KiqrokkzcO7pnkruu0/ZXufuVSogR2rLvPr6ofS/KfZqpPymQi8nlV9bFM9jg6PskZmSQXhz6d5ImWOIG5ecT0J0lurKorMnkD4O8z2eD8jKz/gPuVSb5+M8l883nLJ5EASbr7HVX1+CSvS3LHmY9un+QhI83+V5Lv2cImTsBqPTIH/9370iRv3kZf5yc5d6cBAQCL0d1/W1WPymTz5a+Y+ei4JGeONLs1yfO6+7mLjg+Yr+7+2aq6Osl/ziSJMOuM6c+Y9yb5ju7+m8VEB3ve8Unuu4njfi/JU6bLFm2K+bzlsrQRTE03ZDkryS8luX6DQ/88yTd395NtwgQAALtTd1+R5OFJ/k0myySMuTGThMODJBHg8NXdv5zJPf2LM3nDYMPDk1yQ5ClJHt7dH15weLBXPD/JK5K8P5O3Dw7lukySAI/u7sdvJYlwgPm85SnJFzhYVZ2YyStYZ2aSxbwpyceTvKe7P7LK2ICkqs5N8raZqku7+4xDtPnpJM+ZUwjnd/e5c+oL2ITtjPttnuftSR49U/WU7n7NvM8DLF9VPSCTpxPvnslDdZ9JcmmSP+7ujSYegMPMdH30L8lkzN8pk+WMbk5ydZLLklzQ3VetLkI48lXVSZlM8J+R5G5J9mXy9/fqJFcl+UCSv+zuzSQcNntO83kLJJEAAAAAAACMsrQRAAAAAAAwSiIBAAAAAAAYJZEAAAAAAACMkkgAAAAAAABGSSQAAAAAAACjJBIAAAAAAIBREgkAAAAAAMAoiQQAAAAAAGCURAIAAAAAADBKIgEAAAAAABglkQAAAAAAAIySSAAAAAAAAEZJJAAAAAAAAKMkEgAAAAAAgFESCQAAAAAAwCiJBAAAAAAAYJREAgAAAAAAMEoiAQAAAAAAGCWRAAAAAAAAjJJIAAAAAAAARkkkAAAAAAAAoyQSAAAAAACAURIJAAAAAADAKIkEAAAAAABglEQCAAAAAAAwSiIBAAAAAAAYJZEAAAAAAACMkkgAAAAAAABGSSQAAAAAAACjJBIAAAAAAIBREgkAAAAAAMAoiQQAAAAAAGCURAIAAAAAADBKIgEAAAAAABglkQAAAAAAAIySSAAAAAAAAEZJJAAAAAAAAKP+P34E3aljh5JrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 1800x1800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6, 6), dpi=300)\n",
    "plt.plot(x_values, y_values)\n",
    "plt.grid()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[1.0,\n",
       " 1.0,\n",
       " 0.9999999999999999,\n",
       " 0.9999999999999999,\n",
       " 0.9999999999999999,\n",
       " 0.07102207538289855,\n",
       " 1.254463503866384e-33,\n",
       " 1.254463503866384e-33,\n",
       " 1.254463503866384e-33,\n",
       " 5.389840597697583e-121,\n",
       " 5.389840597697583e-121]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
